The embedding problem with kernel PSL (2, p 2)

The embedding problem of number fields is considered. It is proved that the problem is solvable if and only if all associated local problems corresponding to infinite points are solvable. It is also proved that the solvability of the adjoined problem with Sylow 2-group implies the solvability of the original problem. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 349, 2007, pp. 135–145.